Concept explainers
(a)
The expression for the allowed energies of the electron in terms of the quantum numbers
(a)
Answer to Problem 66P
The expression for the allowed energies of the electron in terms of the quantum numbers
Explanation of Solution
Write the expression for the allowed energy levels of the electron is given by,
Here,
Assuming
Conclusion:
Therefore, the expression for the allowed energies of the electron in terms of the quantum numbers
(b)
The values of
(b)
Answer to Problem 66P
The values of
Explanation of Solution
An electron bound to an atom cannot have any value of energy , it can only occupy certain states which corresponds to certain energy levels.
According to
Conclusion:
Therefore, the values of
(c)
The energy of the ground state.
(c)
Answer to Problem 66P
The energy of the ground state is
Explanation of Solution
The allowed energy is given by,
Conclusion:
Substitute
Therefore, the energy of the ground state is
(d)
The possible values of
(d)
Answer to Problem 66P
The possible values of
Explanation of Solution
The least energy it have is corresponding to
Conclusion:
Therefore, The possible values of
(e)
The possible values of
(e)
Answer to Problem 66P
The possible values of
Explanation of Solution
When the electron is the second excited state the possible values of
Conclusion:
Therefore, The possible values of
(f)
The energy of the second excited state.
(f)
Answer to Problem 66P
The energy of the second excited state is
Explanation of Solution
The possible values of
The allowed energy is given by,
Conclusion:
Substitute
Therefore, the energy of the second excited state is
(g)
The energy difference between the ground state and the second excited state.
(g)
Answer to Problem 66P
The energy difference between the ground state and the second excited state is
Explanation of Solution
The energy difference between the ground state and the second excited state is given by,
Conclusion:
Substitute
Therefore, The energy difference between the ground state and the second excited state is
(h)
The wavelength of a photon which cause the transition between the ground state and the second excited state.
(h)
Answer to Problem 66P
The wavelength of a photon which cause the transition between the ground state and the second excited state is
Explanation of Solution
Write the expression for the energy in terms of wavelength.
Here,
Conclusion:
Substitute
Therefore, the wavelength of a photon which cause the transition between the ground state and the second excited state is
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Chapter 28 Solutions
Principles of Physics: A Calculus-Based Text
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